Math, asked by radhikamalu, 5 months ago

if a and b are are (2,1)and 3,4 respectively find the coordinates of p such tha ap= 4/5 ab and p lies online sengment ab

Answers

Answered by Anonymous
2

Answer:

ꍌ꒐꒦ꏂꋊ:- ꋬ ꒒꒐ꋊꏂ ꇙꏂꍌꂵꏂꋊ꓄ ꒻ꄲ꒐ꋊ꒐ꋊꍌ ꓄ꁝꏂ ꉣꄲ꒐ꋊ꓄ꇙ ꋬ(−2,−2) ꋬꋊ꒯ ꃳ(2,−4). ꉣ ꒐ꇙ ꋬ ꉣꄲ꒐ꋊ꓄ ꄲꋊ ꋬꃳ ꇙ꒤ꉔꁝ ꓄ꁝꋬ꓄ ꋬꉣ=

7

3

ꋬꃳ.

ꋊꄲꅐ,

ꋬꉣ=

7

3

ꋬꃳ(ꍌ꒐꒦ꏂꋊ)

7ꋬꉣ=3(ꋬꉣ+ꃳꉣ)

7ꋬꉣ=3ꋬꉣ+3ꃳꉣ

⇒7ꋬꉣ−3ꋬꉣ=3ꃳꉣ

ꃳꉣ

ꋬꉣ

=

4

3

꓄ꁝꏂꋪꏂꊰꄲꋪꏂ,

ꉣꄲ꒐ꋊ꓄ ꉣ ꒯꒐꒦꒐꒯ꏂꇙ ꋬꃳ ꒐ꋊ꓄ꏂꋪꋊꋬ꒒꒒ꌦ ꒐ꋊ ꓄ꁝꏂ ꋪꋬ꓄꒐ꄲ 3:4.

ꋬꇙ ꅐꏂ ꀘꋊꄲꅐ ꓄ꁝꋬ꓄ ꒐ꊰ ꋬ ꉣꄲ꒐ꋊ꓄ (ꁝ,ꀘ) ꒯꒐꒦꒐꒯ꏂꇙ ꋬ ꒒꒐ꋊꏂ ꒻ꄲ꒐ꋊ꒐ꋊꍌ ꓄ꁝꏂ ꉣꄲ꒐ꋊ꓄ (ꉧ

1

,ꌦ

1

) ꋬꋊ꒯ (ꉧ

2

,ꌦ

2

) ꒐ꋊ ꓄ꁝꏂ ꋪꋬ꓄꒐ꄲꋊ ꂵ:ꋊ, ꓄ꁝꏂꋊ ꉔꄲꄲꋪ꒯꒐ꋊꋬ꓄ꏂꇙ ꄲꊰ ꓄ꁝꏂ ꉣꄲ꒐ꋊ꓄ ꒐ꇙ ꍌ꒐꒦ꏂꋊ ꋬꇙ-

(ꁝ,ꀘ)=(

ꂵ+ꋊ

ꂵꉧ

2

+ꋊꉧ

1

,

ꂵ+ꋊ

ꂵꌦ

2

+ꋊꌦ

1

)

꓄ꁝꏂꋪꏂꊰꄲꋪꏂ,

ꉔꄲꄲꋪ꒯꒐ꋊꋬ꓄ꏂꇙ ꄲꊰ ꉣ=(

3+4

3×(2)+4×(−2)

,

3+4

3×(−4)+4×(−2)

)=(

7

−2

,

7

−20

)

ꁝꏂꋊꉔꏂ, ꓄ꁝꏂ ꉔꄲꄲꋪ꒯꒐ꋊꋬ꓄ꏂꇙ ꄲꊰ ꉣ ꋬꋪꏂ (

7

−2

,

7

−20

)

Answered by Mihir1001
69

\huge{\underline{\bf\red{Questi {\mathbb{O}} n} :}}

 \sf If \: A \: and \: B \: are \: (2,1) \: and \: (3,4) \: respectively, \\  \sf then \:  find \: the \: coordinates \: of \: P \: such \: that \\ \sf AP=\dfrac{4}{5}AB \: and \: P \: lies \: on \: line \: segment \: AB.

\huge{\underline{\: \bf\green{Answ {\mathbb{E}} r}\ \: :}}

  •  \sf P  \equiv  \bigg( \dfrac{14}{5} ,  \dfrac{17}{5}  \bigg)

\Large{\underline{\bf\purple{Giv {\mathbb{E}} n}\ :}}

  •  \sf A \equiv(2,1) \equiv(x_{1}, y_{1})

  •  \sf B \equiv(3,4)\equiv(x_{2}, y_{2})

  •  \sf  \dfrac{AP}{AB}  =  \dfrac{4}{5}

\Large{\underline{\bf\purple{To \ Fi {\mathbb{N}} d}\ :}}

  •  \sf P = (x, y)

\huge{\underline{\bf\blue{Soluti {\mathbb{O}} n}\ :}}

let the ratio b/w AP and AB be 4k : 5k.

Therefore, the ratio between AP and PB will be 4k : k

That is,

 \sf AP : AB = 4k : k

Thus, the point P divides the line segment AB in the ratio 4 : 1.

Thus,

\begin{aligned} \sf P & \equiv( x, y) \\  \\ & \equiv  \bigg[ \frac{ 4x_2 + x_1}{4 + 1} ,  \frac{4y _2 +y_1}{4 + 1}  \bigg]  \\  \\  &\equiv  \bigg[ \frac{ 4(3) + (2)}{5} ,  \frac{4(4) +(1)}{5}  \bigg]  \\  \\ &\equiv  \bigg[ \frac{12 + 2}{5} ,  \frac{16 + 1}{5}  \bigg]  \\  \\ &\equiv  \bigg[ \frac{14}{5} ,  \frac{17}{5}  \bigg]  \\ & & & & & \end{aligned}

\red{\rule{5.5cm}{0.02cm}}

\purple{\rule{7.5cm}{0.02cm}}

\Large{ \mid {\underline{\underline{\bf\green{BrainLiest \ AnswEr}}}} \mid }

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